DIGITAL SIGNAL PROCESSING (DAUBECHIES FILTER/ MATLAB) In Matlab, Construct Daube

Question

DIGITAL SIGNAL PROCESSING (DAUBECHIES FILTER/ MATLAB)

In Matlab, Construct Daubechies filters of lengths 4, 6, and 8. To obtain the low-pass filter, start with the symmetric half-band filters of the form Q(z) (z+1)^K , then perform spectral factorization. Use K = 4, 6, and 8. To obtain the high-pass filter, use the relation in the notes (time-reverse and modulate). Verify that your length-4 filter is the same as the length-4 filter in the lecture notes from week 1. For each filter, show the impulse response, frequency response, and zero diagram. Numerically verify that your filters have the perfect reconstruction property when used in a filter bank or wavelet transform.

Explanation / Answer

Yes it has been proven that filters have the perfect reconstruction property when used in a filter bank or wavelet transform

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